{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VTUIZWAKOJEYJDOGINU2XMJ7VG","short_pith_number":"pith:VTUIZWAK","schema_version":"1.0","canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","source":{"kind":"arxiv","id":"1810.00089","version":1},"attestation_state":"computed","paper":{"title":"Feedback Stabilization Using Koopman Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bowen Huang, Umesh Vaidya, Xu Ma","submitted_at":"2018-09-28T21:40:43Z","abstract_excerpt":"In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.00089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T21:40:43Z","cross_cats_sorted":[],"title_canon_sha256":"2616da76fe32be906911aafc079a483f841aa9c1251c8eb2ed79aeb9eb210751","abstract_canon_sha256":"95ef2013b73c0ab9ab5738aad7ad7eb3e5e4e5f8d3d77ffd846e3c688e2c004a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:28.842983Z","signature_b64":"4g1eMl1e5nU1QytOAVu2A9IefvTyaRT500xXR7HrgXhr+UpoW/BrA2Ky3uHAuZk/7aIAxgeT72iPAp1Kok6AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","last_reissued_at":"2026-05-18T00:04:28.842352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:28.842352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Feedback Stabilization Using Koopman Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bowen Huang, Umesh Vaidya, Xu Ma","submitted_at":"2018-09-28T21:40:43Z","abstract_excerpt":"In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00089","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.00089","created_at":"2026-05-18T00:04:28.842449+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00089v1","created_at":"2026-05-18T00:04:28.842449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00089","created_at":"2026-05-18T00:04:28.842449+00:00"},{"alias_kind":"pith_short_12","alias_value":"VTUIZWAKOJEY","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VTUIZWAKOJEYJDOG","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VTUIZWAK","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG","json":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG.json","graph_json":"https://pith.science/api/pith-number/VTUIZWAKOJEYJDOGINU2XMJ7VG/graph.json","events_json":"https://pith.science/api/pith-number/VTUIZWAKOJEYJDOGINU2XMJ7VG/events.json","paper":"https://pith.science/paper/VTUIZWAK"},"agent_actions":{"view_html":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG","download_json":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG.json","view_paper":"https://pith.science/paper/VTUIZWAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00089&json=true","fetch_graph":"https://pith.science/api/pith-number/VTUIZWAKOJEYJDOGINU2XMJ7VG/graph.json","fetch_events":"https://pith.science/api/pith-number/VTUIZWAKOJEYJDOGINU2XMJ7VG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/action/storage_attestation","attest_author":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/action/author_attestation","sign_citation":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/action/citation_signature","submit_replication":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/action/replication_record"}},"created_at":"2026-05-18T00:04:28.842449+00:00","updated_at":"2026-05-18T00:04:28.842449+00:00"}